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Which type of force is used by your legs to pedal a bicycle?

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A cheetah can run at a maximum speed 97.8 km/h and a gazelle can run at a maximum speed of 78.2 km/h. If both animals are runnin

emmainna [20.7K]

(1)

Cheetah speed: $v_c = 97.8 km/h=27.2 m/s$

Its position at time t is given by

$S_c (t)= v_c t$ (1)

Gazelle speed: $v_g = 78.2 km/h=21.7 m/s$

the gazelle starts S0=96.8 m ahead, therefore its position at time t is given by

$S_g(t)=S_0 +v_g t$ (2)

The cheetah reaches the gazelle when $S_c=S_g$ . Therefore, equalizing (1) and (2) and solving for t, we find the time the cheetah needs to catch the gazelle:

$v_c t=S_0 + v_g t$

$(v_c -v_g t)=S_0$

$t=\frac{S_0}{v_c-v_t}=\frac{96.8 m}{27.2 m/s-21.7 m/s}=17.6 s$

(2) To solve the problem, we have to calculate the distance that the two animals can cover in t=7.5 s.

Cheetah: $S_c = v_c t =(27.2 m/s)(7.5 s)=204 m$

Gazelle: $S_g = v_g t =(21.7 m/s)(7.5 s)=162.8 m$

So, the gazelle should be ahead of the cheetah of at least

$d=S_c -S_g =204 m-162.8 m=41.2 m$

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